But what is the direction of this force?
Perpendicular [down] to surface?

Yes.

So if the surface is tilted at an angle what would the frictional force be?

if your ball hits the surface perpendicularly - the force is as you wrote.
But if you just drop a ball on tilted surface, or throw it at any other angle, you will have combined effect of damping friction (depending on velocity component perpendicular to the surface), friction in motion parallel to the surface, and energy transfer to rotation of your ball.

Is it possible to express frictional force [due to damping] using force due to gravity (on the point of impact) and not velocity?

Nope. Just take extreme case: if you lay your ball on a table (velocity is 0) there is no dumping friction, but gravity is always the same.

if your ball hits the surface perpendicularly - the force is as you wrote.
But if you just drop a ball on tilted surface, or throw it at any other angle, you will have combined effect of damping friction (depending on velocity component perpendicular to the surface), friction in motion parallel to the surface, and energy transfer to rotation of your ball.

Is it possible to express frictional force [due to damping] using force due to gravity (on the point of impact) and not velocity?

Nope. Just take extreme case: if you lay your ball on a table (velocity is 0) there is no dumping friction, but gravity is always the same.

About the angled surface... Ignoring the surface friction, would the damping force decrease by an angle of cos(theta) or something like that?